CS 352: Computer Graphics

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CS 352 Computer Graphics
Hierarchical Graphics, Modeling, And Animation
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Overview

• Modeling
• Animation
• Data structures for interactive graphics
• CSG-tree
• BSP-tree
• Quadtrees and Octrees
• Visibility precomputation
• Many figures and examples in this set of lectures
  are from The Art of 3D Computer Animation and
  Imaging, by I. Kerlow

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Modeling

• The modeling problem
• Modeling primitives
• Polygon
• Sphere, ellipsoid, torus, superquadric
• NURBS, surfaces of revolutions, smoothed polygons
• Particles
• Skin bones
• Approaches to modeling complex shapes
• Tools such as extrude, revolve, loft, split,
  stitch, blend
• Constructive solid geometry (CSG)
• Hierarchy kinematic joints
• Inverse kinematics
• Keyframes

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Representing objects

• Objects represented as symbols
• Defined in model coordinates transformed into
  world coordinates (M TRS)
• glMatrixMode(GL_MODELVIEW)
• glLoadIdentity() glTranslatef()
• glRotatef() glScalef()
• glutSolidCylinder()

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Primitives

• The basic sort of primitive is the polygon
• Number of polygons tradeoff between render time
  and model accuracy

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SplineCurves

• Linear spline
• Cardinal spline
• B-spline
• Bezier curve
• NURBS (non-uniform rational b-spline)

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Mesh
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Mesh deformations
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Sweep

• Sweep a shape over a path to form a generalized
  cylinder

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Revolution

• Revolve a shape around an axis to create an
  object with rotational symmetry

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Extrusion

• Extrude grow a 2D shape in the third dimension
• Shape is created with a (1D)b-spline curves
• Hole was created by subtracting a cylinder

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Joining Primitives

• Stitching, blending

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Modifying Primitives
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Subdivision Surfaces

• Can set level of polygon subdivision

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Skin and Bones

• Skeleton with joined bones
• Can add skin on top of bones
• Automatic or hand-tunedskinning

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Particles
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Algorithmic Primitives
Algorithms for trees, mountains, grass, fur,
lightning, fire,
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Geometric model file formats

• .obj Alias Wavefront
• .dxf Autocad
• .vrml Inventor
• Dozens more
• Can convert between formats
• Converting to a common format may lose info

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Hierarchical models

• When animation is desired, objects may have parts
  that move with respect to each other
• Object represented as hierarchy
• Often there are joints with motion constraints
• E.g. represent wheels of car as sub-objects with
  rotational motion (car moves 2 pi r per rotation)

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DAG models

• Could use tree torepresent object
• Actually, a DAG (directed acyclicgraph) is
  better can re-use objects
• Note that each arrow needs aseparate modeling
  transform
• In object-oriented graphics, alsoneed motion
  constraints with eacharrow

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Example Robot

• Traverse DAG using DFS (or BFS)
• Push and pop matrices along the way (e.g.
  left-child right-sibling) (joint position
  parameters?)

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Modeling Programs

• Moray
• Shareware
• Limited functionality
• Easy
• Lightwave, Maya
• NOT shareware
• Very full-featured
• Difficult to learn and use
• Moray, Maya demos Lightwave video

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Animation

• Suppose you want the robot to pick up a can of
  oil to drink. How?
• You could set the joint positions at each
  moment in the animation (kinematics)

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Inverse Kinematics

• You cant just invert the joint transformations
• Joint settings arent even necessarily unique
  for a hand position!
• Inverse kinematics figure out from the hand
  position where the joints should be set.

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Using Inverse Kinematics

• Specify joint constraintsand priorities
• Move end effector(or object pose)
• Let the system figureout joint positions
• IK demo

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Keyframe Animation

• In traditional key frame animation the animator
  draws several important frames, and helpers do
  the inbetweening or tweening
• Computer animation is also key-frame based
• At key frames, animator positions objects and
  lights, sets parameters, etc.
• The system interpolates parameter values linearly
  or along a curve
• To get from one object pose to the next, inverse
  kinematics determine joint motions
• Keyframe animation demo

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Motion Capture

• More realistic motion sequences can be
  generated by Motion Capture
• Attach joint position indicatorsto real actors
• Record live action

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Morphing

• Morphing smoothly shifting from one image to
  another
• First popularized in a Michael Jackson video
• Method a combination of
• Warping both images, gradually moving control
  points from location in first image to location
  in the second
• Cross-fading from first image sequence to second

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3D Morphing

• Define 3D before andafter shapes as e.g. NURBS
  surfaces with same number ofcontrol points
• Gradually move control points fromfirst setting
  to second
• Specify key poses e.g. smile, frown, 12 frames
  of walking motion

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Combined approaches
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Example virtual puppetry

• Suppose you want to display virtual puppet shows
• How could you animate puppet movements?
• How could you control the animations externally?

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Character Animation

• To make computer graphics(or cartoon drawings)
  come alive

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Personality through Pose, Expression, Motion,
Timing
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Object-oriented Graphics

• Higher in the programming hierarchy control
  models with object-oriented programs
• robot robbie
• robbie.smile()
• robbie.walk(270, 5, 3)

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Data Structures for Modeling

• This part of chapter how some example
  applications be done efficiently (i.e. topics
  without a better home)
• Tree-based subdivisions of space
• Example 1 how to represent complex objects made
  up of union, intersection, difference of other
  objects

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CSG Tree
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Application 2 HSR

• How to render in 3D with hidden surface removal
  when you dont have a hardware depth-buffer?
• Can you think of any other ways of removing
  hidden surfaces quickly?
• Principle a polygon cant be occluded by
  another polygon that is behind it.

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BSP-tree

• The painters algorithm for hidden surface
  removal works by drawing all faces, from back to
  front
• How to get a listing of the faces in
  back-to-front order?
• Put them into a binary tree and traverse the tree
  (but in what order?)

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BSP Tree Figures

• Right is front of polygon left is back
• In and Out nodes show regions of space inside or
  outside the object
• (Or, just store split pieces of polygons at
  leaves)

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Traversing a BSP tree

• Binary Space Partition tree a binary tree with a
  polygon at each node
• Children in left subtree are behind polygon
• Children in right subtree are in front of polygon
• Traversing a BSP-tree
• If null pointer, do nothing
• Else, draw far subtree, then polygon at current
  node, then near subtree
• Far and near are determined by location of viewer
• Runtime of traversal?
• Drawbacks?

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Building a BSP tree

• Inserting a polygon
• If tree is empty make it the root
• If polygon to be inserted intersects plane of
  polygon of current node, split and insert half on
  each side recursively.
• Else insert on appropriate side recursively
• Problem the number of faces could grow
  dramatically
• Worst case (O(n2))but usually it doesnt grow
  too badly in practice

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BSP-tree Summary

• Returns polygons not necessarily in sorted order,
  but in an order that is correct for back-to-front
  rendering
• Widely used when Z-buffer hardware may not be
  available (e.g. game engines)
• Guarantees back-to-front rendering for alpha
  blending
• Works well (linear-time traversals) in the number
  of split polygons
• And we hope the number of polygons doesnt grow
  too much through splitting

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Application 3 Handling Large Spatial Data Sets

• Example application image-based rendering
• Suppose you have many digital images of a scene,
  with depth information for pixels
• How to find efficiently the points that are in
  front?
• Other applications
• Speeding up ray-tracing with many objects
• Rendering contours of 3D volumetric data such as
  MRI scans

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Quadtree

• Quadtree divide space into four quadrants. Mark
  as Empty, Full, or Partially full.
• Recursively subdivide partially full regions
• Saves much time, space over 2D pixel data!

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Quadtree Structure
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Octrees

• Generalize to cutting up a cube into 8 sub-cubes,
  each of which may be E, F, or P (and subdivided)
• Much more efficientthan a 3D array ofcells for
  3Dvolumetric data

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Quadtree Algorithms

• How would you
• render a quadtree shape?
• find the intersection of a ray with a quadtree
  shape?
• Take the union of two quadtrees?
• Intersection?
• Find the neighbors of a cell?

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Applications of Octrees

• Contour finding in MRI data
• 3D scanning and rendering
• Efficient ray tracing
• Intersection, collision testing

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Research in Visibility

• Can we figure out in advance what will be visible
  from each viewpoint?

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Viewer-centered representation

• Viewer-centered object representations
  representation not of volume of space filled but
  appearance from all viewpoints

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Occlusion in view space

• Occlusion in view space is subtraction

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Events

• Events boundaries in viewpoint space where
  faces appear or disappear

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Aspect Graph

• Aspect graph a graph with a node for every
  topologically distinct view of an object, with
  edges connecting adjacent views

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Aspect graph varieties

• Aspect graphs can be constructed for
• 3D space
• 2D multiple axis rotations or planar motions
• 1D single-axis rotations

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1D Aspect Graph for Rotation
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1D Aspect Graph Results

• Useful for rotations without Z-buffer hardware!
• Not so useful for more viewer freedom, modern
  graphics hardware

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Conservative Visibility Preprocessing

• Q. can we take advantage of z-buffer?
• Definition weak visibility. A polygon is weakly
  visible from a region if any part of the polygon
  is visible from any viewpoint in the region
• Conservative visibility preprocessing computing
  in advance a (super-)set of the polygons that are
  weakly visible from some region
• Rendering with Z-buffer yields correct image, but
  its faster since fewer polygons are drawn

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Weak Visibility Subdivision

• Given an object and a wall, find the region of
  space from which the wall occludes the object
• Divide space into regions, where each edge
  represents some object appearing or
  disappearing

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Conservative Visibility Preprocessing on a Grid

• Divide viewing space into a 3D (or 2D) grid
• Compute a conservative display list for each cell

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Conservative visibility algorithm

• Initialize a display list for each grid cell
• Algorithm for each object, wall, and cell
• If the object is not weakly visible from the
  cell, remove from cells display list
• You can churn away at this computation as long as
  you like, increasing runtimes, but you can stop
  at any time with usable results. (Results improve
  over time!)

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Perspective

• What good did this visibility research do for the
  world?
• It wasnt enough for me
• I left graphics research and went into digital
  libraries
• Left University of Pittsburgh and went to Wheaton
  College

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Summary

• 3D modeling uses advanced primitives and ways of
  cutting, joining them
• Inverse kinematics determines joint position from
  end effector motions
• Keyframe animation involves important poses and
  inbetweening
• 3D morphing animates surface control points
• 3D spatial subdivision trees include CSG-trees,
  BSP-trees, Quadtrees, and Octrees
• Visibility preprocessing speeds walkthrough